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On moments of a polytope

Abstract:

We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P ⊂ Rd is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the density function. Using this, we solve the inverse moment problem for the set of, not necessarily convex, polytopes having a given set S of vertices. Under a weak non-degeneracy a...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1007/s13324-018-0226-8

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Computer Science
ORCID:
0000-0002-7557-6886
Shapiro, B More by this author
Shapiro, M More by this author
Publisher:
Springer International Publishing Publisher's website
Journal:
Analysis and Mathematical Physics Journal website
Volume:
8
Issue:
2
Pages:
255–287
Publication date:
2018-04-12
Acceptance date:
2018-04-02
DOI:
EISSN:
1664-235X
ISSN:
1664-2368
Pubs id:
pubs:836665
URN:
uri:2fb84b81-caa1-4a12-891a-e4614200690c
UUID:
uuid:2fb84b81-caa1-4a12-891a-e4614200690c
Local pid:
pubs:836665

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